Fermions and noncommutative emergent gravity II: Curved branes in extra dimensions

We study fermions coupled to Yang-Mills matrix models from the point of view of emergent gravity. The matrix model Dirac operator provides an appropriate coupling for fermions to the effective gravitational metric for general branes with nontrivial embedding, albeit with a non-standard spin connection. This generalizes previous results for 4-dimensional matrix models. Integrating out the fermions in a nontrivial geometrical background induces indeed the Einstein-Hilbert action of the effective metric, as well as additional terms which couple the Poisson tensor to the Riemann tensor, and a dilaton-like term.Comment: 34 pages; minor change

Violation of the phase space general covariance as a diffeomorphism anomaly in quantum mechanics

We consider a topological quantum mechanics described by a phase space path integral and study the 1-dimensional analog for the path integral representation of the Kontsevich formula. We see that the naive bosonic integral possesses divergences, that it is even naively non-invariant and thus is ill-defined. We then consider a super-extension of the theory which eliminates the divergences and makes the theory naively invariant. This super-extension is equivalent to the correct choice of measure and was discussed in the literature. We then investigate the behavior of this extended theory under diffeomorphisms of the extended phase space and despite of its naive invariance find out that the theory possesses anomaly under nonlinear diffeomorphisms. We localize the origin of the anomaly and calculate the lowest nontrivial anomalous contribution.Comment: 36 page

Black-holes, topological strings and large N phase transitions

The counting of microstates of BPS black-holes on local Calabi-Yau of the form ${\mathcal O}(p-2)\oplus{\mathcal O}(-p) \longrightarrow S^2$ is explored by computing the partition function of q-deformed Yang-Mills theory on $S^2$. We obtain, at finite $N$, the instanton expansion of the gauge theory. It can be written exactly as the partition function for U(N) Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. In the large $N$ limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces to the trivial sector and the topological string partition function on the resolved conifold is reproduced in this regime. At a certain critical point, instantons are enhanced and the theory undergoes a phase transition into a strong coupling regime. The transition from the strong coupling phase to the weak coupling phase is of third order.Comment: 16 pages, 3 figures; Invited talk given at QG05, Cala Gonone (Italy), September 200

The role of passion in exercise addiction, exercise volume, and exercise intensity in long-term exercisers

Recent studies have shown a relationship between the risk for exercise addiction (REA) and passion. This research examined whether levels of REA, volume of exercise (in weekly hours), and self-reported exercise intensities yield differences in obsessive passion and harmonious passion among individuals with long history of exercise. Respondents (n = 360) completed the Exercise Addiction Inventory, Passion Scale, and Borg Scale (assessing their usual exercise intensity), and reported their volume of exercise (hours per week). Regression analysis demonstrated that exercise intensity, obsessive passion, and harmonious passion were significant predictors (r2 = .381, p < .001) of the REA scores with obsessive passion being the strongest predictor (r2 = .318). Exercisers classified as at REA reported higher obsessive passion, harmonious passion, and exercise intensity (p ≤ .001) than those classified as symptomatic, who in turn scored higher on these measures (p ≤ .006) than asymptomatic exercisers. Participants reporting greater volumes of exercise also scored higher on obsessive passion, harmonious passion (p < .001), exercise intensity (p = .032), and REA scores (p = .042) than individuals who exercised less. Finally, women exercising between low and high intensities exhibited greater obsessive passion, as well as harmonious passion (p ≤ .005) than men reporting similar exercise intensities. These findings support the recently reported relationship between passion and REA. They also expand the current knowledge by demonstrating that obsessive passion and harmonious passion are greater in the individuals who exercise at higher volumes and with higher intensities

Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds

We develop quantization techniques for describing the nonassociative geometry probed by closed strings in flat non-geometric R-flux backgrounds M. Starting from a suitable Courant sigma-model on an open membrane with target space M, regarded as a topological sector of closed string dynamics in R-space, we derive a twisted Poisson sigma-model on the boundary of the membrane whose target space is the cotangent bundle T^*M and whose quasi-Poisson structure coincides with those previously proposed. We argue that from the membrane perspective the path integral over multivalued closed string fields in Q-space is equivalent to integrating over open strings in R-space. The corresponding boundary correlation functions reproduce Kontsevich's deformation quantization formula for the twisted Poisson manifolds. For constant R-flux, we derive closed formulas for the corresponding nonassociative star product and its associator, and compare them with previous proposals for a 3-product of fields on R-space. We develop various versions of the Seiberg-Witten map which relate our nonassociative star products to associative ones and add fluctuations to the R-flux background. We show that the Kontsevich formula coincides with the star product obtained by quantizing the dual of a Lie 2-algebra via convolution in an integrating Lie 2-group associated to the T-dual doubled geometry, and hence clarify the relation to the twisted convolution products for topological nonassociative torus bundles. We further demonstrate how our approach leads to a consistent quantization of Nambu-Poisson 3-brackets.Comment: 52 pages; v2: references adde

Multiple D4-D2-D0 on the Conifold and Wall-crossing with the Flop

We study the wall-crossing phenomena of D4-D2-D0 bound states with two units of D4-brane charge on the resolved conifold. We identify the walls of marginal stability and evaluate the discrete changes of the BPS indices by using the Kontsevich-Soibelman wall-crossing formula. In particular, we find that the field theories on D4-branes in two large radius limits are properly connected by the wall-crossings involving the flop transition of the conifold. We also find that in one of the large radius limits there are stable bound states of two D4-D2-D0 fragments.Comment: 24 pages, 4 figures; v2: typos corrected, minor changes, a reference adde

An Integrated Approach Providing Scientific and Policy-Relevant Insights for South-West Bangladesh

Bangladesh is identified as an impact hotspot for sea-level rise in multiple studies. However, a range of other factors must be considered including catchment management, socio-economic development and governance quality, as well as delta plain biophysical processes. Taking an integrated assessment approach highlights that to 2050 future changes are more sensitive to human choice/policy intervention than climate change, ecosystem services diminish as a proportion of the economy with time, continuing historic trends and significant poverty persists for some households. Hence under favourable policy decisions, development could transform Bangladesh by 2050 making it less vulnerable to longer-term climate change and subsidence. Beyond 2050, the threats of climate change are much larger, requiring strategic adaptation responses and policy changes that must be initiated now

A possible method for non-Hermitian and non-PTPT-symmetric Hamiltonian systems

A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator $\eta_+$ and defining the annihilation and creation operators to be $\eta_+$-pseudo-Hermitian adjoint to each other. The operator $\eta_+$ represents the $\eta_+$-pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-$PT$-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator $\eta_+$ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-$PT$-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution) are found not to be altered by the noncommutativity.Comment: 15 pages, no figures; v2: clarifications added; v3: 16 pages, 1 figure, clarifications made clearer; v4: 19 pages, the main context is completely rewritten; v5: 25 pages, title slightly changed, clarifications added, the final version to appear in PLOS ON

Wall-crossing of D4-D2-D0 and flop of the conifold

We discuss the wall-crossing of the BPS bound states of a non-compact holomorphic D4-brane with D2 and D0-branes on the conifold. We use the Kontsevich-Soibelman wall-crossing formula and analyze the BPS degeneracy in various chambers. In particular we obtain a relation between BPS degeneracies in two limiting attractor chambers related by a flop transition. Our result is consistent with known results and predicts BPS degeneracies in all chambers.Comment: 15 pages, 4 figures; v2: typos corrected; v3: minor changes, a reference added, version to be published in JHE

Refined Chern-Simons theory and (q, t)-deformed Yang-Mills theory : Semi-classical expansion and planar limit

We study the relationship between refined Chern-Simons theory on lens spaces S-3/Z(p) and (q, t)-deformed Yang-Mills theory on the sphere S-2. We derive the instanton partition function of (q, t)-deformed U(N) Yang-Mills theory and describe it explicitly as an analytical continuation of the semi-classical expansion of refined Chern-Simons theory. The derivations are based on a generalization of the Weyl character formula to Macdonald polynomials. The expansion is used to formulate q-generalizations of beta-deformed matrix models for refined Chern-Simons theory, as well as conjectural formulas for the chi(y)-genus of the moduli space of U(N) instantons on the surface O(-p) -> P-1 for all p >= 1 which enumerate black hole microstates in refined topological string theory. We study the large N phase structures of the refined gauge theories, and match them with refined topological string theory on the resolved conifold